How to estimate the impact of policy on labor supply if the policy causes death, too? Suppose people can make only one of three choices A, B, C.
A = Death
B = Survive, Work
C = Survive, Not work

I want to study the impact of an exogenous policy on people's choice.
Regression 1: I first estimate the impact of the policy on choosing A (i.e. death)
Regression 2: I estimate the impact of policy on choosing B over C.
But for Regression 2, since I cannot observe dead people's work, here the sample is those who didn't die (i.e. those who didn't choose A)
One could argue that survivor bias was introduced. But still, one might say that, by taking regression 1 and 2, we get the whole picture. Is that possible? Or how else could I estimate the true impact of the policy?
 A: I agree with Henry, this framing seems a little unusual. That being said, if the outcome variable of interest is work vs. no work, you are indeed suffering from sample selection bias due to truncation if your sample includes both those who die and those who survive.
You will want to run a 2-stage Heckman correction (Heckman, 1979). There are lots of resources on this method online. Here, in the first stage you will estimate the likelihood of death, and in the second stage  you will estimate the likelihood of working.
Your theory must therefore predict what factors determine the likelihood of death. These are the variables you will include in the first stage of your Heckman correction. You need to have at least one instrument variable in the first stage that predicts the likelihood of death the first place and not affecting likelihood of working. This will help you develop a valid exclusion restriction in the selection equation. See this paper for a robust explanation of why your predictors in both stages must differ to get more accurate estimates.
If you  are implementing this in Stata, also consider heckprobit, since you  likely have a binary dependent variable (work).
Good luck.
